# Advanced Modeling Programs: Introduction to the THERMOCALC Mineral Equilibria Modeling Software

## What is it?

THERMOCALC is thermodynamic calculation software for tackling mineral equilibria problems. It has two main components: the application itself, and the internally-consistent thermodynamic dataset it uses. The mineral equilibria problems that can be addressed with THERMOCALC include *inverse modeling* ones (geothermometry/barometry using average *PT*), and *forward modeling* ones (calculating phase diagrams for model systems). For the latter there exists a program - drawpd - that allows manually assembled THERMOCALC output to be drawn in postscript.

## Principles

In the application of equilibrium thermodynamics to the calculation of phase diagrams, there are two approaches that can be followed: one based on the minimization of Gibbs energy, the other being a derivative equivalent based on the solution of sets of non-linear equations. The main non-linear equations involved are the "equilibrium relationships": the relationships for balanced chemical reactions between the end-members of phases that are in equilibrium with each other:

*G*+R

_{o}*T*ln

*K*

In this, Δ*G _{o}* is the Gibbs energy of the reaction between the pure end-members in the same structure as the phases in which they occur,

*K*is the equilibrium constant, in terms of the activities of the end-members in their phases,

*T*is temperature, and R is the gas constant. THERMOCALC follows this non-linear equation approach.

## Applications

### Phase Diagram Calculations

**Projections** show stable invariant points and univariant reaction lines for all of the bulk compositions in a model system (e.g. petrogenetic grids) (Fig. 1). **Compatibility diagrams** show the mineral assemblages and ranges of mineral solid solutions at a specified P and T, for all the bulk compositions in the model system (e.g. AFM diagrams) (Fig. 2). **Pseudosections** show just those phase relationships for a specified bulk composition (Fig. 3). Axes can be P and T, or may reference a particular bulk composition line X (Fig. 4).

**Fig. 1.**P-T projection for KFMASH (+mu + q + H

_{2}O); the in-excess phases are not included in the reactions labeling the univariant lines, as is usual for such diagrams.

*Click image to enlarge.*

**Fig. 2.**AFM compatibility diagram for KFMASH (+mu + q + H2O) at P = 6 kbar and T = 560°C.

*Click image to enlarge.*

**Fig. 3.**P-T pseudosection in KFMASH (+mu+q+H2O) for a "common" pelite composition: Al

_{2}O

_{3}= 41.89, MgO = 18.19, FeO = 27.29, and K

_{2}O = 12.63 (in mol%).

*Click image to enlarge.*

### Average PT Calculations

With the existence of thermodynamic data for a wide range of end-members in rock-forming minerals, thermobarometry may involve combining many equilibria to find the PT of formation of a rock. In finding a PT of formation, there is an implied displacement of the equilibria to coincide with this PT. These displacements are mainly made by varying the activities of the end-members of the minerals, in proportion to their uncertainties. As a consequence, the equilibria are constrained to move in a more or less highly correlated way because the equilibria involve overlapping subsets of the end-members. These essential correlations should be included in any thermobarometry calculations. Such an optimal approach allows PT, their uncertainties, and a range of diagnostics for outlier identification, to be calculated in a computationally inexpensive way.

## Strengths & Limitations

Univariant reactions in a petrogenetic grid are extremely useful in providing bounding constraints on the stability of mineral assemblages. However, petrogenetic grids, especially complex ones with lots of reactions, can be difficult to interpret, and most mineral assemblages in real rocks are higher variance. Moreover, for specific rock compositions, many of these reactions are not 'seen' by a particular bulk composition.

Most people are interested in specific mineral assemblages in the rocks they are studying, for which they have collected and analyzed. The advantage of the pseudosection approach is that this type of diagram portrays only the reactions we are interested in by examining a compositional slice through the full multi-component chemical system.

One caveat of the pseudosection approach is the choice of bulk composition. This can be done via a whole rock geochemical (XRF) analysis if equilibrium is achieved on the 'rock' scale. However, many metamorphic rocks preserve chemical zoning of porphyroblasts and the choice of an 'effective' bulk composition is more appropriate, by combining mineral chemistry data with modal proportions (e.g. by only including garnet cores and excluding the rims).

## Worked Examples

### Phase Diagrams

The basic approach to setting up a problem in THERMOCALC involves the following sequence of steps:

- Choose a model system in which to do the calculations
- Formulate the thermodynamics (a-X relationships) of the phases in the system
- Decide which phase diagrams are to be constructed and, for pseudosections, choose an appropriate bulk composition:
- P-T Projections
- Compatibility Diagrams
- P-T Pseudosections
- P-X or T-X Pseudosections
- Build up the phase diagram via calculations on the equilibria involved

### Average PT

## References

- Holland, TJB, & Powell, R, 1998. An internally-consistent thermodynamic dataset for phases of petrological interest. Journal of Metamorphic Geology 16, 309-344.
- Holland, TJB, & Powell, R, 2003. Activity-composition relations for phases in petrological calculations: an asymmetric multicomponent formulation. Contributions to Mineralogy and Petrology 145, 492-501.
- Powell, R, 1978. Equilibrium Thermodynamics in Petrology Harper and Row, 284 pp.
- Powell, R, Guiraud, M, & White, RW, 2005. Truth and beauty in metamorphic mineral equilibria: conjugate variables and phase diagrams. Canadian Mineralogist, 43, 21-33.
- Powell, R, & Holland, TJB, 1988 An internally consistent thermodynamic dataset with uncertainties and correlations: 3: application methods, worked examples and a computer program. Journal of Metamorphic Geology 6, 173-204.
- Powell, R, & Holland, TJB, 1994. Optimal geothermometry and geobarometry. American Mineralogist 79, 120-133.
- Powell, R, Holland, TJB, & Worley, B, 1998. Calculating phase diagrams involving solid solutions via non-linear equations, with examples using THERMOCALC Journal of Metamorphic Geology 16, 577-588.
- Worley, B, & Powell, R, 1999. High-precision relative thermobarometry: theory and a worked example Journal of Metamorphic Geology 18, 91-102.

## Related Links

- Roger Powell's THERMOCALC Page
- Tim Holland's THERMOCALC Page
- Links to THERMOCALC resources from Dave Waters' Thermobarometry webpage.

## Teaching Activities

- Multi-equilibrium Thermobarometry Lab (Microsoft Word 53kB Mar29 07) - This Excel-based one week exercise, provided by Dave Pattison at the University of Calgary, includes problems sets involving multi-equilibrium thermobarometry using TWQ and ThermoCalc's 'AvePT' module ('Optimal thermobarometry').

## Roger Powell's THERMOCALC Short Course, 2006

These are the files of presentations and problem sets presented at the Granulites 2006 short course in Sao Paulo, Brazil.

### Short Course Lecture Presentations

- First Principles, Definitions and an Introduction to ThermoCalc (Acrobat (PDF) 1.2MB Aug29 07) by Roger Powell
- Phase Diagrams, Equilibrium, PTX Relations, Projections and Sections, Variance and Compatibility Diagrams (Acrobat (PDF) 1.1MB Aug29 07) by Roger Powell
- Pseudosections (Acrobat (PDF) 883kB Aug29 07) by Roger Powell
- Chemical Systems, Phase Diagrams Tips and Tricks (PowerPoint 4.6MB Aug29 07) by Richard White
- Thermobarometry and (many) Uncertainties (Acrobat (PDF) 1.8MB Aug29 07) by Roger Powell

### Documents, Tutorials, Examples

- Overview of Documents (Acrobat (PDF) 127kB Aug30 07) presented at the 2006 ThermoCalc Short Course; (the documents that are refered to in this document can be accessed through the links below).
- Background
- Introduction to Phase Diagrams (Acrobat (PDF) 310kB Aug30 07); includes terminology, Schreinemakers, Balancing Reactions and Projections.
- Internally Consistent Thermodynamic Datasets (Acrobat (PDF) 432kB Aug30 07); including data from Holland and Powell (1998, Jour. Metamorph. Petrol.), and an extensive bibliography.
- Activity-Composition Relationships (Acrobat (PDF) 65kB Aug30 07)
- Calculating Mineral Equilibria (Acrobat (PDF) 51kB Aug30 07)
- ThermoCalc
- Introduction to ThermoCalc (Acrobat (PDF) 46kB Aug30 07)
- Datafile Construction (Acrobat (PDF) 197kB Aug30 07)
- Script Documentation (Acrobat (PDF) 102kB Aug30 07)
- Calculationg Phase Diagrams with ThermoCalc (Acrobat (PDF) 168kB Aug30 07)
- Average PT (Acrobat (PDF) 55kB Aug30 07)
- ThermoCalc Website based on Powell et al (1998) (Acrobat (PDF) 622kB Aug30 07), showing graphical user interface, directions for running ThermoCalc, and annotated examples of ThermoCalc programs.
- DrawPad
- Construction of DataFiles for DrawPad 1.0 (Acrobat (PDF) 57kB Aug30 07)
- Worked example using DrawPad (Acrobat (PDF) 43kB Aug30 07)
- Activity composition (A-X)
- Introduction to the A-X Program (Acrobat (PDF) 41kB Aug30 07); includes mineral end-member activity models.
- Practical Examples (Pracs)
- Practical Example 1 (Acrobat (PDF) 41kB Aug30 07)
- Solution to Practical Example 1 (Acrobat (PDF) 36kB Aug30 07)
- Practical Example 2 (Acrobat (PDF) 40kB Aug30 07)
- Solution to Practical Example 2 (Acrobat (PDF) 72kB Aug30 07)
- Phase Diagram Movies (Way Cool!)
- AFM Movie at 3 Kb, 500-580
^{o}C (Quicktime Video 476kB Aug30 07) - AFM Movie at 6 Kb, 500-560
^{o}C (Quicktime Video 585kB Aug30 07) - AFM Movie at 3 Kb, 544-557
^{o}C; chloritoid-out reaction (Quicktime Video 356kB Aug30 07) - AFM T-X Section at 5-10.5 Kb (Quicktime Video 1.8MB Aug30 07)
- Movies based on Worley, B, and Powell, R, 1998. Singularities in the system Na
_{2}OCaOK_{2}OMgOFeO Al_{2}O_{3}SiO_{2}H_{2}O. Journal of Metamorphic Geology 16, 169-188. - NCFM System, 5.5 Kb, 555-560
^{o}C; margarite-in reaction (Quicktime Video 105kB Aug30 07) - NCFM System, 5.5 Kb, 586-591
^{o}C; paragonite-in reaction (Quicktime Video 132kB Aug30 07) - NCFM System, 5.5 Kb, 596-601
^{o}C (Quicktime Video 167kB Aug30 07) - NCFM System, 5.5 Kb, 590-610
^{o}C; staurolite-kyanite isograd (Quicktime Video 499kB Aug30 07) - NCFM System, 5.5 Kb, 605-610
^{o}C (Quicktime Video 115kB Aug30 07) - NCFM System, 5.5 Kb, 550-670
^{o}C (Quicktime Video 735kB Aug30 07) - Other Useful Information Related to ThermoCalc
- Summary of notation used in Powell et al (1998) (Acrobat (PDF) 93kB Aug30 07); including symbols for thermodynamic calculations, mineral abbreviations, and end-member mineral formulae.
- Datafile names for ThermoCalc and DrawPad (Acrobat (PDF) 30kB Aug30 07)
- Example Phase Diagrams that can be Calculated with ThermoCalc (Acrobat (PDF) 256kB Aug30 07)
- Drawing Phase Diagrams with Mathematica Using Output Data From ThermoCalc (Acrobat (PDF) 188kB Aug30 07)
- Recommended Reading–Articles that provide background an greater understanding related to ThermoCalc (Acrobat (PDF) 60kB Aug30 07)
- General References on Heterogeneous Phase Equilibria (Acrobat (PDF) 171kB Aug30 07)

**You will need to upload QuickTime to view these movies!**